A study explores weight changes in high school students during the pandemic. Let X = change in weight (positive means weight gain). For a sample of n = 19 teens, the changes in weight during the study were: -8, -6, -6, -4, -3, 0, 3, 6, 6, 8, 10, 11, 13, 13, 14, 14, 15, 16, 16 with x =6.21 lbs and s=8.37 lbs

Hypotheses:

H0:=0 (The average change is zero)

H_a: 0 (The average change is not zero)

Where = mean change in weight for all high school students during the pandemic

Show ti-84 commands if necessary

#1. Conditions We will assume that this is a random sample and it seems likely that 19 is less than 10% of the population of high school students. On your own paper, use a dotplot and explain how the sample data indicates that it is reasonable to assume that the population weight change is approximately normal. Take a picture of your work and upload it where indicated.

#2. Mechanics Because the population standard deviation is unknown, we must use a t-procedure. In the space below write the formula for the t-statistic with appropriate values in place of all variables. Then use your calculator test menu to find the ultimate value of t and the associated P-value.

#3. Make your decision linked in context (use alpha = 5%):

Use your calculator to find a 95% confidence interval to estimate the mean change in weight and write the interval in the space below.

#4. Briefly explain how your interval in part (1.4) supports the decision you made in part (1.3).